What's the difference between a monograph and an article ?
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SureshApr 12 '14 at 19:53

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@Suresh: A monograph is a research article which is so long that it has been published as a book. The refereeing process may also be different. Certainly one wonders whether for a 300 page manuscript, every page has been read with the same care as for a 30 page manuscript.
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Pete L. ClarkApr 12 '14 at 20:21

@PeteL.Clark: Is a monograph an article? AMS refused my book proposal saying that there are too much conjectures in my work to be published as a monograph. Conjectures are not a problem with an article however. So a monograph is not just a long article, their conditions of review are different.
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portonApr 12 '14 at 20:36

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@porton: As a matter of definition, no, a monograph is a book rather than an article. The goals of a monograph are however similar to those of an article. With regard to your deductions about the differences between articles and monographs based on the rejection of your monograph by the AMS: it would seem that you first need to have equivalent content published in AMS journals in order to reason in this way.
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Pete L. ClarkApr 12 '14 at 22:21

One example is Dicks and Dunwoody Groups acting on graphs. This gives the first published proof of the Almost Stability Theorem, and currently has 152 citations on mathscinet.
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Shane O RourkeApr 13 '14 at 11:31

1 Answer
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Research monographs in mathematics certainly exist, but they aren't the standard form of publication. They are generally not as prestigious as papers in strong mainstream journals, they may be less widely read, and they may be viewed as being less carefully refereed. Some important work in mathematics has first been published in monograph form, but I wouldn't recommend it unless you have a very good reason (for example, extremely long proofs, or lots of valuable material that would be harder to understand or appreciate out of context).

There are some journals that publish extremely long papers in monograph form, such as Memoirs of the American Mathematical Society. If you want to publish a research monograph in mathematics, a series like this is a reasonable place for it, while a stand-alone book is riskier.